YES

Problem:
 a__and(tt(),X) -> mark(X)
 a__plus(N,0()) -> mark(N)
 a__plus(N,s(M)) -> s(a__plus(mark(N),mark(M)))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
 mark(tt()) -> tt()
 mark(0()) -> 0()
 mark(s(X)) -> s(mark(X))
 a__and(X1,X2) -> and(X1,X2)
 a__plus(X1,X2) -> plus(X1,X2)

Proof:
 DP Processor:
  DPs:
   a__and#(tt(),X) -> mark#(X)
   a__plus#(N,0()) -> mark#(N)
   a__plus#(N,s(M)) -> mark#(M)
   a__plus#(N,s(M)) -> mark#(N)
   a__plus#(N,s(M)) -> a__plus#(mark(N),mark(M))
   mark#(and(X1,X2)) -> mark#(X1)
   mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
   mark#(plus(X1,X2)) -> mark#(X2)
   mark#(plus(X1,X2)) -> mark#(X1)
   mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2))
   mark#(s(X)) -> mark#(X)
  TRS:
   a__and(tt(),X) -> mark(X)
   a__plus(N,0()) -> mark(N)
   a__plus(N,s(M)) -> s(a__plus(mark(N),mark(M)))
   mark(and(X1,X2)) -> a__and(mark(X1),X2)
   mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
   mark(tt()) -> tt()
   mark(0()) -> 0()
   mark(s(X)) -> s(mark(X))
   a__and(X1,X2) -> and(X1,X2)
   a__plus(X1,X2) -> plus(X1,X2)
  KBO Processor:
   argument filtering:
    pi(tt) = []
    pi(a__and) = [0,1]
    pi(mark) = [0]
    pi(0) = []
    pi(a__plus) = [0,1]
    pi(s) = [0]
    pi(and) = [0,1]
    pi(plus) = [0,1]
    pi(a__and#) = [0,1]
    pi(mark#) = [0]
    pi(a__plus#) = [0,1]
   weight function:
    w0 = 1
    w(mark#) = w(plus) = w(and) = w(s) = w(a__plus) = w(0) = w(a__and) = w(
    tt) = 1
    w(a__plus#) = w(a__and#) = w(mark) = 0
   precedence:
    a__plus# ~ mark > a__and > a__and# ~ a__plus > mark# ~ plus ~ and ~ s ~ 0 ~ tt
   problem:
    DPs:
     
    TRS:
     a__and(tt(),X) -> mark(X)
     a__plus(N,0()) -> mark(N)
     a__plus(N,s(M)) -> s(a__plus(mark(N),mark(M)))
     mark(and(X1,X2)) -> a__and(mark(X1),X2)
     mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
     mark(tt()) -> tt()
     mark(0()) -> 0()
     mark(s(X)) -> s(mark(X))
     a__and(X1,X2) -> and(X1,X2)
     a__plus(X1,X2) -> plus(X1,X2)
   Qed